In: Finance
Today’s price of Delta Airlines (DAL) is $30 per share. DAL does not pay dividends. The annualized volatility of DAL is 45 percent. The c.c. risk-free interest rate is ten percent. Assume there is no arbitrage and the Black-Scholes model assumptions hold.
What is the price of a European put option on DAL with a strike of $40 and a maturity of one year?
Solution>
The price of the European put option is $9.48
I have solved it in Excel. The formula used are written in the column along with the values. If you still have any doubt, kindly ask in the comment section.
| Type of Option | Put Option | |
| Stock Price (S0) | $ 30.00 | |
| Exercise (Strike) Price (K) | $ 40.00 | |
| Time to Maturity (in years) (t) | 1.00 | |
| Annual Risk Free Rate (r) | 10.00% | |
| Annualized Volatility (σ) | 45.00% | |
| Option Price | $ 9.48 | =K*e-rt*N(-D2)-S0*N(-D1) | 
| Additional Calculation Parameters | ||
| ln(S0/K) | (0.288) | |
| (r+σ2/2)t | 0.201 | |
| σ√t | 0.450 | |
| d1 | (0.192) | =(ln(S0/K)+(r+σ2/2)t)/σ√t | 
| d2 | (0.642) | =D1-σ√t | 
| N(d1) | 0.424 | =NORM.S.DIST(d1) | 
| N(d2) | 0.260 | =NORM.S.DIST(d2) | 
| N(-d1) | 0.576 | =NORM.S.DIST(-d1) | 
| N(-d2) | 0.740 | =NORM.S.DIST(-d2) | 
| e-rt | 0.90484 | 
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